SPATIOTEMPORAL SELF-ORGANIZATION IN A MODEL OF DISEASE SPREADING

We investigate an extended version of the probabilistic Forest-Fire model conceived as a model of disease spreading. We show that the model self-organizes spatially and temporally from random initial conditions into a well-defined state with a characteristic length and time scale. The time scale tau has a power-law dependence on the correlation length xi, ie., tau similar to xi with a non-trivial exponent of approximate to 0.83 in d = 2. We show that stochastic input of susceptible individuals is essential for this behaviour. A mean field approximation is presented, predicting an exponent of z = 1/2.